PROJECT TITLE :

A Generalized Signature of Repairable Coherent Systems

ABSTRACT:

We present a generalized signature in repairable coherent systems resembling Samaniego's notion for statistically independent and identically distributed lifetimes. The repairable systems are created of different components which can individually fail, and be minimally repaired up to a fixed range of times. Failures occur consistent with Poisson processes, which would possibly have either the identical intensity function for each element, or different ones. The former case is almost like the notion of signature presented by Samaniego for i.i.d. random variables, whereas here statistically independent Poisson processes with identical intensity functions are thought of. An express expression for computing the generalized signature of repairable series systems is obtained. It is shown that the reliability function of any repairable coherent system will be expressed as a generalized mixture of the chances of the quantity of repairs until system failure. We additionally establish that the stochastic ordering between the generalized signatures of two repairable systems is preserved by their lifetimes.